Optimal design under unknown information is a key task in process systems engineering. This study considers formulations that incorporate two types of unknown input parameters, uncertain model parameters, and variable process parameters. In the former case, a process must be designed that is feasible over the entire domain of uncertain parameters, while in the latter case, control variables can be adjusted during process operation to compensate for variable process parameters. To address this problem we extend the two-stage formulation for design under uncertainty and derive new formulations for the multiperiod and feasibility problems. Moreover, to simplify the feasibility problem in the two-stage algorithm, we also introduce a KS constraint aggregation function and derive a single, smooth nonlinear program that approximates the feasibility problem. Three case studies are presented to demonstrate the proposed approach.